The fans that left early also missed a red card shown to Villa defender Alan Hutton in the 85th minute that sealed another miserable afternoon for the home side.
The significance of the 74th-minute protest is that Villa were founded in 1874 and banners hoisted in protest were targeted at American owner Randy Lerner while others read: "Proud History, What Future?".
The immediate future for the seven-times champions of England will be in the Championship next season as the club, who parted company with manager Remi Garde on Tuesday, are stranded at the bottom of the Premier League with 16 points from 32 matches and no realistic chance of survival.
Villa's caretaker manager Eric Black said after another dreadful display it was important to win back the faith of the fans.
Asked if that could happen, he replied: "It's got to happen, and it will. How quickly, I don't know.
"When the team is bottom of the league I can understand the disconnect with the supporters. We have to give the supporters something, not the other way round. It's been a hard season for them."
Chelsea, champions last season, have also under-performed this term, spending most of the campaign in mid-table, but have now gone 15 matches unbeaten since Jose Mourinho left the club in December.
Villa's defeat was their seventh in a row in the league.
Loftus-Cheek scored his first league goal to put Chelsea ahead before Pato, the former AC Milan starlet who has been kicking his heels since joining from Corinthians two months ago, netted with a penalty on his debut at the end of the first half.
Pato, known as 'The Duck', broke his duck by picking himself up after being fouled by Aly Cissokho to convert from 12 metres.
Pedro then added his two goals in the opening 14 minutes of the second half.
(Reporting by Ian Chadband, editing by Ed Osmond)
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